Supplemental Materials
The Value of Vengeance and the Demand for Deterrence
By M. J. Crockett et al., 2014, Journal of Experimental Psychology: General
http://dx.doi.org/10.1037/xge0000018
Experimental Procedure
All interactions in the experiment were fully anonymous. We collected the decisions of participants in the role of T and B in advance of the main experiment. These decisions were collected at the end of other experimental sessions in the Economics Laboratory by paper-and-pencil. These participants were instructed that their decisions could be matched with future participants in the role of player P, and that they would receive the money resulting from the subsequent use of their decisions via post. We employed this procedure so that we could present participants in the role of player P with a set of decisions that displayed specific parameters, but without using deception. All aspects of the procedure were fully transparent to all participants (i.e., no deception was used).
In the main experiment, participants in the role of player P first read a set of detailed instructions and completed a comprehension quiz, which had to be passed successfully in order to continue with the experiment. Importantly, to pass the quiz, P players had to correctly answer questions that indicated whether they understood that in the hidden condition T players could not know whether they had been punished. All participants passed the comprehension quiz.
Next, each participant decided whether to entrust their initial endowment of CHF 5 to all players in the role of T that they would face during the entire experiment. Subjects who entrusted the CHF 5 then played a series of 54 anonymous one-shot trust games with punishment, each with different individuals in the roles of B and T. Since we collected the decisions of B and T players in advance, we were able to face each player P with the same set of 54 parameterizations, reflecting a factorial within-subjects design that crossed (a) T’s back transfer to B (0%, 25%, or 50%), (b) T’s back transfer to P (0%, 25%, or 50%), (c) whether T's intentional decision affected P, B, or neither; and (d) whether punishment was open or hidden (see Figure S1). We only selected B players who decided to entrust the CHF 5 to the trustee T.
In each game, the initial entrusted endowment of CHF 5 was multiplied by 4. This multiplier was known to players P and B but not player T. Next, participants viewed the information about the current trial. Finally, participants received an additional endowment of CHF 5 and decided how much to spend to reduce the payoff of player T. Each CHF 0.10 spent on punishment reduced the payoff of player T by CHF 0.20. Participants had unlimited time to make their decisions.
Player T was informed that the multiplier m could lie in the range of 2 to 6. However, m was always kept constant at 4 such that Player T was never able to infer whether he has been punished from his final payoff alone.
Punishment motive questionnaire
After the decision-making phase, all participants filled out an electronic questionnaire. We examined post-hoc self-reported punishment motives by measuring agreement with the following 7 statements using a 5-point Likert scale:
I reduced the payoff of the punisher …
1. … because it was fun.
2. … to teach him a lesson.
3. … because I wanted him to suffer.
4. … to change his future behavior.
5. … to reduce inequality.
6. … to demonstrate my power.
7. … to take revenge.
With these ratings, we conducted a principal components analysis with varimax rotation and Kaiser normalization. This revealed two independent factors with eigenvalues greater than one, accounting for 66% of the total variance in the ratings. The first factor, deterrence, accounted for 35% of the variance and included items 2, 4, and 5. The second factor, retribution, accounted for 32% of the variance and included items 1, 3, 6, and 7.
For the correlation analyses reported in the main text, we computed means of the retribution and deterrence items to derive retribution and deterrence scores for each subject. The questionnaire also included items about the quality of the instructions as well as the age and educational level of the participants.
Figure S1. Summary of factorial design. Participants in the role of the punisher who entrusted the CHF 5 in the first stage passed through 54 treatments, each a particular combination of the information condition, the intentionality, the back transfer to P, and the back transfer to B.
Payoff and Information Structure of the Trustee
By tightly controlling the information available to T, we were able to ensure that in the hidden punishment condition T could not reasonably infer whether he has been punished. A low overall payoff for T could, for example, be due to (i) a low multiplier or (ii) a high computer-driven back transfer or (iii) a certain punishment level. However, because T knows nothing about these three variables, he cannot make any reasonable inferences about the punishment level (see SI for a detailed explanation).
In this section we show that in the hidden condition the Trustee can never infer from his final payoff that he has been punished. First define the following variables:
· Multiplier: m ∈ M = [2, 6]
· Impact of punishment: p ∈ P = [0, 10]
· Intentional back transfer decision of the Trustee: i ∈ I = {0, 0.25, 0.5}
· Back transfer decision of the computer: j ∈ J = {0, 0.25, 0.5}
· Payoff of the Trustee: π = 5m(1 – i) + 5m(1 – j) – p = 5m[2 – (i+j)] – p
· Information set of the Trustee in the hidden condition: S = {i, I, J, M, P, π}
The realization of the multiplier and the back transfer decision of the computer were unknown to the Trustee. Hence, from the perspective of the Trustee each of the three intentional back transfer decisions lead to a different range of possible payoffs:
(1.1) π(i = 0) ∈ [15 – p, 60 – p]
(1.2) π(i = 0.25) ∈ [12.5 – p, 52.5 – p]
(1.3) π(i = 0.5) ∈ [10 – p, 45 – p]
The ranges in (1.1)-(1.3) are calculated by combining the range of the multiplier with the possible back transfer decisions of the computer, holding the intentional back transfer, which is known to the Trustee, constant. The lower bound of each range in (1.1)-(1.3) results from the lowest possible multiplier, m = 2, and the highest possible back transfer decision of the computer, j = 0.5. The upper bound of each range in (1.1)-(1.3) results from the highest possible multiplier, m = 6, and the lowest possible back transfer decision of the computer, j = 0.
Since the multiplier was, however, kept constant at m = 4, the following payoffs might have actually occurred, depending on the intentional back transfer decision, the back transfer decision of the computer and the punishment decision[1]:
(2.1) π(i + j = 0, m = 4) = 40 – p
(2.2) π(i + j = 0.25, m = 4) = 35 – p
(2.3) π(i + j = 0.5, m = 4) = 30 – p
(2.4) π(i + j = 0.75, m = 4) = 25 – p
(2.5) π(i + j = 1, m = 4) = 20 – p
With a sufficiently low payoff the Trustee could theoretically infer that p was larger than zero if the trustee earns less than the lower bound in (1.1 – 1.3) for p=0. Thus, a positive level of p could only be inferred if the following occurred:
(3.1) π(i = 0) < 15
(3.2) π(i = 0.25) < 12.5 or
(3.3) π(i = 0.5) < 10
If, for example, the Trustee had decided to transfer back i = 0 and had obtained a payoff smaller than 15 it would have been possible to infer that p > 0 based on (1.1). But by (2.3) the lowest possible payoff that might have actually occurred, if i = 0, was 30 – p. This follows from the fact that i + j cannot be larger than 0.5, if i = 0. However, since the punishment technology did not allow p to be larger than 10, the actual payoff for i = 0 could have never been lower than 20. Therefore, the actual payoff in this scenario could have never been lower than 15, the threshold value given by (3.1), and thus the Trustee cannot infer that he has been punished, if i = 0.
Now we show that this argument also holds for i = 0.25 and i = 0.5. Table S1 depicts for each combination of i and j the required punishment impact such that the actual payoff given by (2.1)-(2.5) would be lower than the corresponding threshold value given by (3.1)-(3.3). Because in all scenarios p ∈ [0, 10] is too low to sufficiently decrease the actual payoff, the Trustee can never deduce that he has been punished, unless the information is explicitly provided.
Table S1
Required Impact of Punishment Such That the Trustee Could Infer That He Has Been Punished
Appendix 1
Instructions and Quiz
Instructions
Player P instructions
You are now participating in an experiment which is sponsored by various research foundations. The experiment is completed in cooperation with the Department of Economics at the University of Zurich, Switzerland. Please read the following instructions carefully. If you have any questions, please ask an experimenter.
You will receive a fixed amount of CHF 25 for participation in this experiment. You can also earn money in addition to this fixed amount based on your decisions during the experiment. Upon conclusion of the experiment, you will receive your payment in cash.
These instructions are solely reserved for your private information. Communication is strictly forbidden during the study. If you have any questions, please ask us. Disregarding these rules leads to exclusion from the experiment and from any payments.
The data collected in this experiment will be kept strictly confidential. Future publications only represent average results. Drawing inference on particular participants will not be possible, and your anonymity will be maintained at all times.
There are three types of participants in this experiment, participants A, participants B, and participants C. You are a Participant A. Participants B and C have already made their decisions and are, therefore, not present in the lab today. We will further explain to you the background of this procedure in the last section. You will be matched sequentially with a group of 54 different pairs of people who are in the role of participant B and participant C.
You will participate in a three-step experiment with each of the 54 pairs of participant B and participant C. You will interact with each participant only once. Consequently, you will interact with 108 different people in this experiment: 54 participants B, and 54 participants C. The whole experiment will be completely anonymous. Neither will you know the identity of any other participant, nor will any other participant know your identity.
The experiment consists of three steps. On the following pages we will explain you these three steps and the exact procedure of the experiment. The payoffs on the following pages are related to those payoffs which you can earn in addition to the fixed payment of CHF 25.
Procedure for the three steps. You and participant B will each receive an endowment of CHF 5 at the beginning of the experiment.
Independent from each other, you both must decide in step one whether you want to transfer your endowment of CHF 5 to Participant C or if you will transfer nothing.
If you decide to transfer the CHF 5, it will be multiplied by the factor 4, meaning that Participant C will receive a total endowment of CHF 20. So if both you and Participant B transfer the CHF 5 to Participant C, he will receive CHF 20 from you and CHF 20 from Participant B. Participant C knows whether you and Participant B transferred the CHF 5 to him or not. But he is not informed about the factor with which each of the CHF 5 are multiplied. He only knows that the multiplier lies in a range between 2 and 6. Therefore, Participant C does not know the amount which he receives from you and Participant C after the multiplication.
If you decide not to transfer the CHF 5, you will keep the CHF 5 and you will not participate in the following steps of the experiment. If Participant C does not receive any CHF 5 in step one, his payoff for this round will be CHF 0. The following diagram illustrates possible money flows in step one:
Example for Step 1
There will be two decisions made in step two:
(1) Participant C will send back to you 0%, 25%, or 50% of what he received from you.
(2) Participant C will send back to Participant B 0%, 25%, or 50% of what he received from Participant B.
Sometimes one of these decisions will be made by Participant C, and the other will be made by the computer. At other times, both decisions will be made by the computer. Participant C will never learn the decision made by the computer.
Note that Participant C will make his decisions about the percentage of the endowment he will transfer back to you and Participant B. Since he is not informed about the factor with which each CHF 5 is multiplied, Participant C does not know the size of the total endowment at the time he makes his decision.